ASM FM1 - Practice Exam] ' A We at. -...

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Unformatted text preview: Practice Exam] ' A We at. - mama-g.rzmwmemm..:.;agnw .. a, .. Note to Snidents: As we said in the Introduction, most students think that the five original practice exams that follow are more difficult than actual past exams. (We think it’s a good idea to practice on problems that are a little harder, on average, than the real thing.) So don’t be discouraged if you don’t do too well on these exams. Do all of the problems that you don’t get right a couple of days later under time pressure to make sure that you have learned how to solve them. These practice exams follow the format of the actual exams in 2008: 35 questions in three hours. The actual exam will be in CBT format. Several of the questions (perhaps five) will be pilot questions that will not be graded, but you will have no way of knowing which ones they are. When you take these exams, stick to the time limit and simulate exam conditions. Questions for Practice Exam 1 1. Harvey is repaying a loan of 1000 with annual payments of 120 for 10 years followed by annual payments of 100 for as long as necessary. The amount of interest in the first payment is 100 and the amount of interest in the 12th payment is X. Determine X. (A) 63 (B) 65 (C) 75 (D) 78 (E) 80 2. A company buys a 100 par value bond with 5% annual coupons. The company pays a price that will give it a yield rate of 4% effective if the bond matures at par at the end of 7 years. The company receives all coupons when due. However, at the end of 7 years, the company receives a maturity value of only 90, due to the bankruptcy of the issuer of the bond. The company’s effective annual yield rate over the 7—year period is 1'. Determine z'. (A) 0.92% (B)1.37% (C) 2.24% (D) 2.73% (E) 3.23% 3. A stock with a current price of $82 will pay no dividends in the coming year. The premium for a one- year European call is $10424 and the premium for the corresponding put is $8.993. The risk-free interest rate is 5.5% effective per annum. X is the strike price of both the call and the put. Determine X to the nearest $1.00. (A) $82 (B)$83 (C) 3584 (D)$85 (E) $86 4. A bond with 100 par value and annual coupons at coupon rate r is redeemable at par at the end of 25 years. The bond is purchased at a price that will earn 5% effective. The write—up in the 15th year is 1.17. Determine r. (A) 3.00% (B) 3.23% (C) 6.95% (D) 7.00% (E) 7.25% 5. Hugh invests 1000 in a fund on January 1. On May 1, the fund is worth 1100 and 600 is withdrawn. On September 1, the fund is worth 400 and 600 is deposited. On January I of the following year, Copyright © 2009 ASM. 9111 edition 637 638 10. 11. 12. 13. 14. 15. Practice Exam 1 - the fund is worth 1200. Hugh’s dollar—weighted rate of return for the year (computed using simple interest from the date of each payment) is X. His time—weighted rate of return is Y. DetermineX — Y. (A) —6.05% (B)5.00% (C) 7.00% (D) 19.40% (E) 25.00% Jan gives Ted a loan at 4% effective to be repaid by 10 annual payments of 100, followed by 5 annual payments of 200. Just after Ted makes the 5th payment, Jan and Ted discover that each of the 15 payments should have been 10% higher than they were originally scheduled. They agree that Ted will make increased payments of K in the 6th through 10th years to adjust for the error. The payments of 200 in the 11th through 15th years will not change. Determine K. (A) 113 (B) 129 (C) 139 (D) 145 (E) 149 Harvey invests X in a fund earning 4% effective per annunm. In return, he receives 1 at the end of each quarter in the first year, 2 at the end of each quarter in the second year, . . . , and 20 at the end of each quarter in the 20th year. Determine X. (A) 127 (B) 453 (C) 508 (D) 554 (E) 1016 Percy invests continuously at a rate of 100 per annum for 40 years in a fund earning 5% per annum compounded continuously. At the end of 60 years, X is in the fund. There are no withdrawals. Determine X . (A) 12778 (B) 25395 (C) 34735 (D) 48832 (E) 62386 . Matilda invests a single deposit of 1000 for 3 years. In the first year, the nominal rate of discount is 8% compounded quarterly. In the second year, the force of interest is 8%. In the third year, the force of discount is 5%. At the end of 3 years, Matilda’s investment is worth X. Determine X. (A) 1050.42 (B) 1071.86 (C) 1105.62 (D) 1234.68 (E) 1237.86 Carl invests 1000. He receives interest on his investment at the end of each year for 10 years at an effective rate of 1'. Carl reinvests the interest at an effective rate of it. At the end of 10 years, the total of Carl’s original investment and the accumulated value of his reinvested interest is 1400. Determine i. (A) 2.67% (B) 3.54% (C) 4.37% (D) 4.70% (E) 5.82% Joe’s annual salary increases by p% every year. The mean of his annual salary for the last 10 years is 1.182 times the mean of his annual salary for the last 20 years. Determine p. (A) 1.25 (B) 2.25 (C) 3.25 (D) 3.75 (E) 5.38 George invests 4000 in a fund. Six months later, he invests 3000 in the same fund. One year from the date of the first investment, the fund has grown to 10000. The fund‘s rate of return is X per annum compounded semiannually, X > 0. Determine X. (A)2.5% (B)5% ((3)2591: (D)50% (E)100% Sylvia is repaying a loan of X by making 17 annual payments of 100. Each payment consists of interest on the loan at 5% effective and an amount that is deposited in a sinking fund earning 4% effective. At the end of 17 years, the amount in the sinking fund is equal to the original loan amount accumulated with interest at the sinking fund rate. Determine X . (A) 721 (B) 756 (C) 818 (D) 1085 (E) 1127 Paul deposits 500 in an account on January 1, 2003. Interest is credited each year on December 31, at a rate of 4% on the first 1000 in the account on January 1 of that year and 5% of any excess over 1000. J ust after interest is credited on December 31, 2032, X is in the account. Determine X. (A) 1580 (B) 1591 (C) 1615 (D) 1622 (E) 1660 Arrange in order of increasing annual effective rate of interest: Copyright © 2009 ASM, 9th edition - Questions for Practice Exam 1 _ (i) An effective rate of interest of 4% per annum. (ii) A force of interest of 4% per annum. (iii) A nominal rate of interest of 4% per annum convertible semiannually. (iv) A nominal rate of discount of 4% per annum convertible semiannually. (A)i,iii,iv (BliiiinLii (Cliiiiaiv (D)iV.i (E) iviiiiiiii 16. A bond with 5% coupons is purchased to yield 4% effective. The amount for amortization of premium (write dowu) in the 15th year is 0.80. The total write down in the first 9 years is X. Determine X . (A) 4.70 (B) 4.89 (C) 6.11 (D) 10.30 (E) 10.71 17. A 39—year annuity—immediate will pay 13 in each of the first 3 years, 12 in each of the next 3 years, etc., until payments of 1 are made in each of the last 3 years. The present value of the annuity payments at an annual effective rate of 3% is X. Determine X . (A)59 (B) 165 (C) 177 (D)184 (E) 187 18. Henry is repaying a loan at an effective rate of 5% a year. The payments at the end of each year for '10 years are 1000 each. In addition to the loan payments. Hemy pays premiums for loan insurance at the beginning of each year. The first premium is 0.5% of the original loan balance, the second premium is 0.5% of the loan balance immediately after the first loan payment, etc., and the tenth premium is 0.5% of the loan balance immediately after the 9th loan payment. The present value of the premiums at 5% is X . Determine X. (A) 132 (B) 158 (C) 163 (D) 197 (E)228 19. Jan buys an annuity at a price X that will give her a yield rate of 5% effective. The annuity consists of 10 payments at 3 year intervals, first payment on date of purchase. The first annuity payment is 100, and each successive payment is 5% greater than the previous one. Determine X. (A) 464 (3)564 (C) 629 (D) 670 (E) 729 20. The force of interest at time I is .0212 Katie invests 1000 at r = 0 and withdrawals 1000 at r = 1. At r = 2, X is in the fund. Deteimine X. (A) 10.15 (B) 10.25 (C) 10.36 (D) 10.46 (E) 10.57 21. Shirley invests 1000 in a fund on January 1. On July 1, 600 is in the fund and Shirley invests X. On December 31, 1625 is in the fund. Shirley determines that her dollar—weighted rate of return for the year is 10% and that her time-weighted rate of return is Y. Determine Y. (A) -—13.3% (B) —I 1.4% (C) 35.4% (D) 62.5% (E) 95.0% 22. The following is a table of interest rates credited under the investment year method. Unfortunately, a few entries are missing: Calendar Year Investment Year Rates Portfolio of Original ___— Rates Investment y 1'); 1% 1% 9’” 1992 5.2% — 4.8% 4.3% 1993 4.2 4.7 4.0 —- 1994 — 5.5 5 .7 5.1 Copyright © 2009 ASM, 9th edition 639 Practice Exam 1 — It is known that an investment of $1,000 in 1992 will accumulate to $1,270.15 at the end of five years and that an investment of $1,000 in 1993 will accumulate to $1,247.33 at the end of five years. Calculate 11:992. (A) 4.4% (B) 4.6% (C) 4.9% (D) 5.0% (E)5.6% 23. The duration of a perpetuity—immediate with level annual payments is 10 years at an effective rate of interest 1'. Determine z'. (A) 1.0% (B) 10.0% (C) 11.1% (D) 37.0% (E) 46.4% 24. The following table shows the current term structure of interest rates: Length of Investment in Years Interest Rate 1 X 2 X + .01 3 3.0% 4 3.4% 5 3.7% The one-year deferred one-year forward rate implied by these rates is 3.5%. Find X. (A) .82% (B) 97% (C) 1.13% (D) 1.28% (E) 1.49% 25. The rate of inflation is a constant 7‘ per annum. A 10-year annuity—immediate provides for annual payments that increase with inflation. The first payment is 1,000(1 + r). The present value of this annuity at 7% effective is $8,056. Determine r. (A) 2.25% (B) 2.50% (C) 2.75% (D) 3.00% (E) 3.25% 26. The current selling price of an asset is $60. Sharon creates a 60—70 collar using two of the 6-month European options in the following table: Strike Price Call Premium Put Premium $60 $6.09 $4.01 70 2.42 9.99 The risk—free nominal rate of interest is 7.2% compounded semiannually. X is the profit on the collar for a spot price at expiration of $77. Determine X. (A) --$21.04 (B) —$8.64 (C)—$.34 (D)$.34 (E)$21.04 27. Shelly buys a one-year 90—strike European call for a premium of $13.17. At the same time, she writes a one—year 70-strike European put on the same underlying asset for a premium of $1 .80. The risk-free interest rate is 6% effective per annum. For a spot price at expiration of X, Sally‘s total profit on the two options combined is —$16.35. Determine X. (A) $37.78 (B) $51.74 (C) $65.70 (D) $70.48 (BLT-98.40 28. X is the bid price of Stock A. X is also the ask price of Stock B. The bid—ask spread for both stocks is 33.25 per share. The broker’s commission is $8 per transaction. Carly buys 100 shares of Stock A and sells 50 shares of Stock B. Her net cash outflow for these two transactions combined is $2,178.50. Determine X. 640 Copyright © 2009 ASM, 9th edition - Questions for Practice Exam 1 (A)$40.72 (B) $41.68 (C) $42.50 (D) $42.34 (E) $43.30 29. Mel sells 100 shares of a stock short on January 1 of Year 1’ and closes his short position the following January 1. The following table shows the bid and ask prices for the stock: January 1, Year Y January 1, Year Y + 1 Bid $70.00 $60.00 Ask 70.25 60.25 There is a $20 broker’s commission on each transaction. On the date of the short sale, Mel is required to deposit a haircut equal to 50% of the transaction amount. He earns 4% effective on the haircut. A dividend of $4 per share is payable on December 31 of Year Y . X is Mel‘s yield rate on this transaction. Determine X. (Assume no interest on the proceeds of the short sale.) (A) 19.3% (B) 20.7% (C) 21.1% (D) 21.5% (E) 22.9% 30. Cynthia buys a share of stock for $150. At the same time, she creates a 150—155 collar as insurance against declines in the price of the stock over the next year. To create the collar, she uses two of the options in the following table showing one-year European options: Strike Price Call Premium Put Premium $150 $22.47 $12.98 155 20.10 15.30 The risk—free interest rate is 6.75% effective per annum. What is Cynthia’s total profit on the stock and the collar combined if the spot price at expiration is $143? (A) —$62.57 (ID—$36.79 (C) -$l4.53 (D) —$9.49 (E) —$2.53 31. You decide to provide yourself with a retirement account by depositing $1,000 into an account at the beginning of each month for the next 35 years. At the end of that 35—year period, you use your entire accumulated account to purchase a 30-year annuity—immediate that pays $75,000 per year. Assume that the effective annual rate of interest is 6% for the first 35 years, and i% thereafter. Find 1'. (A) 3.25 (B) 3.50 (C) 3.75 (D) 4.00 (E) 4.25 32. Assume the following interest rate environment: i=8% for05r<2 5, =0.015: for2 5 t < 5 d=6% for55r<8 it” = 10% fort 3 8 Find the present value of an asset which will pay you a single cash flow of 1,000 at time I = 10. (A) 439 (B) 459 (C) 479 (D) 499 (E) 519 33. The current price of a share of Stock B is $80.00. You enter into a prepaid forward contract on Stock B by paying X now, and one year later you receive a share of Stock B, priced at $95. Stock B pays dividends at a continuous rate of 4% per annum. The continuously-compounded interest rate is 6% per annum. Determine X. (A) 75.34 (B) 76.86 (C) 80.00 (D) 89.47 (E) 91.27 Copyright © 2009 ASM, 9111 edition 641 642 34. 35. Practice Exam 1 - You expect to receive a payment of $1,000 two months from now, and another payment of $2,000 four months from now. Calculate the effective annual interest rate, 1', at which these future payments have a present value of $2,900. (A) 1' 5 12.5% (B) 12.5% <i512.7% (C) 12.7% < 1' 5 12.9% (D) 12.9% <i513.1% (E) 13.1% < 1' On January 1, 2007, Abby sold a share of stock A short for a price of 80. On that same date, Ben sold a share of stock B short for a price of P. Both Abby and Ben bought back and returned, to the original owners, their respective shares of stock on December 31, 2007, when the per-share price of stock A was 70, and the per—share price of stock B was 120. At the end of 2007, just prior to the close of the short position, stock B paid a dividend of 2 per share, while stock A paid no dividend. Both Abby and Ben were subject to a margin requirement of 50%, and interest on the margin accounts was credited at an annual effective rate of 3%. During 2007, Abby’s short sale transaction had an annual effective yield of 35,, and Ben’s transaction had an annual effective yield of 1-3. The relationship between the two yields was r3 = —2rA. Calculate P. (A174 (3)84 (C) 94 (D) 104 (E)ll4 Copyright © 2009 ASM, 9th edition Solutions to Practice Exam 1 Solutions to Practice Exam 1 1. Since the amount of interest in the first payment is 100, we have i = 100/1000 = 10%. To determine the interest in the 12th payment, determine the outstanding balance at the end of the 11th year retrospectively and multiply by 10%. B” = 1000(1.1)ll — (12031—11 — 20) = 2353.17 — 2203.74 = 649.38 112 = (0.1)(64938) = 64.94. ANS. (B) 2. The price the company paid for the bond is 5:25] + 100v7 at 4% = 106.00. (On the BA-35: TE] 5 10 ) We need the value off that satisfies the equation 106 = 5ea + 90v7. oh the BA-35, just enter 9 , keeping all of the previous entries the same. This gives 1' = 2.73%. ANS. (D) 3. We use put-call parity: Call(K, T) — Put(K. T) = PV(F0.T e K) The PV of the forward price for a stock with no dividends is just the current stock price. Substituting, we have: 10.424 — 8.993 = 8?. — K/I.OSS K = $35 ANS. (D) 4. The write—up (or “negative principal repaid”) in the r-th year is given by (Ci — Fr)v”‘"+l. In this case, 1.17 = [(100)(0.05) — 100)‘]17b_15+1 or 1.17 = (5 — 100m” at 5% _ 5 —1.17(1.05)11 = 3.00% ANS. (A) 100 I. 5. If the dollar-weighted rate of return is X , we have: 2 I 1000(1+X) — 600 (1+ EX) + 600 (1+ 3X) = 1200 _ 200 x_ _ 800 = 25% For the time-weighted rate of return, we use the technique shown in Section 5e of the manual. Jan. I May 1 Sept. 1 Jan, 1 1. Fund before deposit/withdrawal 0 2. Deposit/withdrawal +1.000 ~600 +600 3. Fund after deposit/withdrawal m 1+ Y = (1100) (400) (g) = (1.1)(0.8)(1.2) = 1.056 1000 300 1000 Y = 5.6% X — Y=25%—5.6%219.4% ANS. (D) Copyright © 2009 ASM. 9th edition 643 644 Practice Exam 1 . The annual payments should have been 110 in the first 10 years, followed by 220 in the last 5 years (i.e., 10% higher than originaHy scheduled.) The PV of these payments at 4% (Le, the amount of the loan) is: 2200a — 1 10am The PV of the corrected payments is: 200mm — am) + K(am — 05') + 100a§| Setting these PVs equal and solving for K, we get: 200B ‘1‘ 900ml — 100a§| am - a3] K = 138.60 ANS. (C) . The simplest approach is to determine the equivalent effective rate j per quarter: (1 + 1')“ = 1.04 j = 1.04i — 1: .985340653% Using the “block payment” approach per Section 3e of the manual, we have X=20am—afiI—afl—-~—amatratej 19—1'4+iIB+--- v76 =20am_£_<_*+fl J 1,4_l,au =90“ _ h .. 'STJI j which can also be written as: 19 — Ll“? “m X = 20am — I J 19 _ w = (20)(55.17006) _ A 0098534065 2 1103.40 — 595.33 = 508.07 If we had stayed with the original effective annual rate of 4%, X would have the form: 5 — 20v20 X = 4(Ia)% =4 at 4% where 1(4) = 4(I.O4i — 1) = .0394136. (See Section 4i of this manual.) Of course, this expression forX results in the same numerical value of 508.07. ANS. (C) . Note that a nominal rate compounded continuously is the same thing as the force of interest. Thus, 6 = 5%. The AV of this continuous annuity (taking into account the fact that it is to be computed at Copyright © 2009 ASM. 9th edition _ Solutions to Practice Exam 1 a point that is 20 years after the investments stop) can be expressed as: X: 1005a 4551) at8=5% e(.05)(5a) _ 1_ (gamma) _ 1) =100 —— .05 = 2000(e3 — e) = 34735 ANS. (C) 9. At a nominal rate of discount of 8% compounded quarterly, the accumulation factor for one year —4 is ( — = .98‘4. (Note the negative exponent for accumulating with a discount rate.) In the second year, the accumulation factor is 2'03. Since the force of discount is equal to the force of interest, the accumulation factor in the third year is 9'05. The AV of 1000 is thus: X = (1000)(.9s)-4(e-“8)(e-°5) = 1000(.98)—“(e-l3) = 1234.68 ANS. (D) 10. The AV at the end of 10 years of the reinvested interest is lOOOism at if. This must be equal to 400. since the total AV of 1400 consists of the original investment of 1000 and the AV of the reinvested interest. 10 (1+ gt) — 1 1000i 3 = 400 —i 4 IO 3 (1+ —1') = 13 4 3. —: = 2.658360%: 4 i: 3.54% ANS. (B) 11. If S was Joe’s salary 20 years ago, the mean of his annual salary for the last 20 years is: 20 20 S1+(l+p%)+(1+p%)2+...+(1+p%)19 Ss’7 —.——___= —0| at 11% The mean of his salary for the last 10 years is: s[(1+p%)1°+(1+p%)“+---+(1+p%)19] _S.52—01—Sm at ‘7 10 10 p 0 We are given that the ratio of these two means is 1.182: Copyright © 2009 ASM. 9111 edition 645 646 12. 13. 14. Practice Exam 1 sfil—Sfil 10 _ a 52—7)] — 1.18.. 20 (Sm — m) 1.182 5m 2 So 11‘ = 2.4449878 3161 Now S 10' = (1 +12%)10 +1 Sm Therefore, (1 + 13%)10 = 1.4449878. Using the calculator, p = 3.75. ANS. (D) The equation of value is: "D X _ 4000 (1+ ;) + 3000 (l + = 10000 .- For convenience, let (1+ = y. 4y2+3y—10=0 (4y-5)(y+2)=0 (or use the quadratic formula). Taking the positive root: 4y—5=0, y=l.?'.5=1+‘:—f X=.50=50% ANS.(D) The interest included in each payment is .05X. The rest of the payment, (100 — .OSX), is deposited in the SF. The AV of the SF deposits is (100 — .05X)sfilvm. Based on the given information, this is equal to 1.0417X. (100 — .05X)smm = 1.04”): X IOOSfiI'M _ 1.0417 + uni—7134 which can be evaluated as is, or in the equivalent form: 100 a 1 + .05 film X: The arithmetic gives X = 756.44. ANS. (B) This situation may be thought of as withdrawing any amount in excess of 1000 at the end of each year from a 4% account and depositing this excess in a 5% account. The first thing to do is to determine when the 4% account first exceeds 1000. Copyright © 2009 ASM, 9th edition Solutions to Practice Exam 1 500(104’) = 1000 l.04’=2 17<t< 18 Thus, at the end of 18 years (on 12/31/20), there is 5000.04)18 = 1012.91 in the 4% account. Then 12.91 is “withdrawn” and “deposited” in the 5% account. Each year thereafter, 4% x 1000 = 40 is “withdrawn” from the 4% account and “deposited” in the 5% account. The account value on 12/31/2032 is the sum of: (a) 1000 (b) The AV at 5% of 12.91 for 12 years (from 12/31/2020 to 12/31/2032), or 12.91(1.0513) = 23.18. (c) The AV at 5% of annual “deposits” of 40 for 12 years (“deposits” on 12/31/2021 to 12/31/3032), eraosEl at5% = 636.69. Thus, the AV on 12/31/2032 is 1659.87. ANS. (E) 15. We know that dc) < 6 < in) < 1' at the same rate of interest. This fact permits us to order the given rates. For example, if i = .04, 8 < .04 and hence a force of interest equal to .04 implies an annual effective rate greater than .04. By similar reasoning I < [[1 < H < IV. ANS. (A) 16. Although we are not given the term of the bond, the redemption value, etc., we can easily answer this question by making use of the fact that the write downs are in geometric progression with common ratio (1 + i). If the write down in the 15th year is 0.80, the sum of the write downs in the first 9 years is given by: X = 0.130094 + v13 +- - - + W) at 4% = — (15') = 4.89 ANS. (B) Note: We did not even have to know the frequency of coupon payments. This is because the write down in any periodic coupon is (1+i) times the write down in the periodic coupon paid one year earlier, so the sum of the write downs in each calendar year also forms a geometric series with common ratio (1 + i). 17. Using the “block payment” approach (see Section 3c of this manual): PVzafii—afiI—iw “+03 =(1—v39)+(1—v36)+~-+(1—v3) which could be expressed as: 14039 13 ._ “ill (1+03—1 _ ‘El 1' 1' l3— PV: (It is not essential to get it in this form but it does make the calculation a little easier.) PV = 187.36 ANS. (E) 18. The first premium is (-005)(1000)am, the second is (.005)(1000)a§', etc., and the 10th is (.005)(1000)an. The PV of these premiums is: Copyright 2009 ASM, 9th edition 647 648 19. 20. 21. Practice Exam 1 _ 9 PV=5(afi|+va§l+~-+va-fl) l—vw 12—1210 119—1i10 =5( , + _ +---+ . ) l 1 I _5(1+v+---+v9— 101:1”) _ .05 =100(a:fiI — 10.10) = 100(8.1078 — 6.1391) = 196.87 ANS. (D) Note: The expression am + mg + - - - + vgafl is the PV of a 10-payment annuity plus the PV of a one—year deferred 9-payment annuity, etc., plus the PV of a 9-year deferred l-payment annuity. ii —10v10 This adds up to the PV of an increasing 10—payment annuity, which is L. Thus, the same result as above can be obtained by general reasoning (if you are lucky enough to see this under exam conditions). The PV of the payments is: PV = 1000 + 1.05113 + 1.0531;6 + - - - + 1.05%”) at 5% =100(l+v2+v4+---+vlg This is the sum of a geometric progression: _ ,210 _,20 zloou (17) 121000 1) l—v- l—v- PV = 670 Alternatively, it can be seen that the sum represents the PV of an annuity—due of 100 paid every 2 years, or 100%. ANS. (D) E First, find the accumulation function: ’ 1 . .2 r 2 a“) = efu 0.111: = 6,01; 10 = 8.01: Thus, the AV at time 2 of the investment of 1000 at time 0 is 1000e<50m32> = 1000.2-04 = 1040.81. We now have to deduct the AV at time 2 of the withdrawal of 1000 at time I. Here we have to be careful not to fall into the variable force of interest trap. (See Section lg of this manual.) The AV of the withdrawal is j .04 1000fl = 10009— : 1000e-03 = 1035.45 (1(1) 2‘01 Thus, the amount remaining at time 2 is 1,040.81 — 1035.45 = 10.36. ANS. (C) First, we determine the deposit X: 10000 + i) +X (1 + = 1625 where 1' is given as 10%. From this, X = 500. Then set up a schematic. (See Section 5c of this manual.) Copyright © 2009 ASM, 9th edition _ Solutions to Practice Exam 1 Jan. 1 July 1 Dec. 31 1. Fund before deposit/withdrawal 0 2. Deposit/withdrawal +I,000 +500 3. Fund after deposit/withdrawal 1,000 m If Y is the time-weighted rate of return, we have: 7 1+Y= (390—) (E =.886 1000 1100 Y=—.114=—11.4% ANS. (B) 22. (1) 1000(1.052)(1+ £21993)(1.048)(l.043)(1+ 11996) = 1,270.15 (2) 1000(1.042)(1.047)(1.040)(1 +11996)(1.051) = 1,247.33 Therefore, 1+ 11995 = 1.046. Substituting in (1) and solving: 1 + if” = 1.056 and 1:993 = 5.6%. ANS. (E) 23. Duration is the weighted-average time, where the weights are the present values of the payments: 6? = 2 NR, 2 "(Rr In this case: &_ 1r+2112+3v3+--- _ 11+1r2+v3+... = (1(035] “El 1 . (RUM = it andaa = 1- 1 5' = = 10 1 l 1=6=.111=11.1% ANS.(C) 61(3) . __ z 1 “(1) +1 (See Section 9b of this manual.) 2 (1 +X + .01) :1-035 1+X X2 + .985X * .0149 = 0 X _ _ .985 + #9853 — 4(—.0149) _ _2* = 1.49% ANS. (E) Note: The spot rates for 3~year, 4-year and 5-year investments have no bearing on the one-year deferred one-year forward rate. Copyright © 2009 ASM, 9111 edition 649 650 Practice Exam 1 25. The PV of the annuity is: 2 10 1+r l—l—r l+r 8,056 = 1,000 —— + . .. _ [1.07 +(I.O7) +(l.07) :| The expression in brackets is the PV of a level annuity at an adjusted rate of interest. (See Section 4j of this manual.) This can be seen more clearly if we let i” = %. The expression in brackets becomes: where 1+ 1" — 1'07 or i’ = '07 _ r _ 1 + r 1+ 1- We have 8,056= 1,000amip Using the calculator, enter N = 10, PMT = 1,000, PV = 8,056, then CPT %i. We get i = 4.136651%. Since 1+ i’ = fig, 1‘ = 2.75% ANS. (C) 26. A 60—70 collar is created by buying a 60—strike put and selling a 70-strike call. V! + (vi): + _ _ _ + (1,!)10 zamf’ Profit on purchased 60-snike put = max[0, 60 — 77] — FV (premium) = —(4.01)(1.036) = —$4.15 Profit on written "I'D—strike call: — max[0, 77 — 70] + FV (premium) 2 —7 + (2.42)(1.036) = —$4.49 Profit on collar = —4.15 — 4.49 = —$8.64 ANS. (B) 27. Consider three ranges for X: X < 70, 70 < X < 90 and X > 90. For X < 70: Profit on 90-sn'ike purchased call = max[0, X — 90] — FV (premium) = —(13.07)(1.06) = —13.96 Profit on 7O—st1‘ike written put: — max[0, 70 — X] + FV (premium) = -(70 — X) + (l.80)(1.06) =X — 68.09 Total profit: —13.96 + X -— 68.09 = —16.35 X = $65.70 ANS. (C) Note: We did not consider the other ranges for X (Le, 70 < X < 90 and X > 90) once we found a value for X that was consistent with X < 70. (You will find that if you try the other ranges, there will be an inconsistency.) 28. (You have to be careful: The ask price for Stock A is (X + .25) and the bid price for Stock B is (X —— .25).) Buy Stock A: (100)(X + .25) -{- 8 = IOOX + 33 Sell Stock B: (50) (X — .25) — 8 = 50X — 20.50 Net cash outflow = 100X + 33 — (50X — 20.50) = 2, 178.50 X = $42.50 ANS. (C) 29. The proceeds from the short sale are (100)(70) — 20 = $6, 980. The haircut = 50% x 6, 980 = $3, 490. Interest on the haircut = (.04) (3,490) = $139.60. Dividends payable to lender of stock = (100) (4) = $400. Purchase price of stock to cover the short = (100)(60.25) + 20 = 6045. Copyright © 2009 ASM. 9th edition Solutions to Practice Exam 1 Net gain at the end of one year = 139.60 — 400 + (6,980 — 6,045) = $674.60. Yield rate = 674.60/3, 490 = 19.3% ANS. (A) 30. (If we buy a stock and create a collar, this position is called a “collared stock”.) A 150—155 collar is created by buying a ISO—strike put and selling a lSS—strike call. Profit on Stock itself: 143 — (150)(l.0675) = —$I7.13 Profit on purchased ISO-strike put: max[0, 150 — 143] -— FV (premium) = 7 - (12.98)(1.0675) = —$6.86 Profit on written lSS—strike call = — max[0, 143 ~— 155] + (20.10)(1.0675) = $21.46 Total profit: — l 7.13 — 6.86 + 21.46 = —$2.53 ANS. (E) 31. This is a common type of question, where you accumulate (through the first 35 years, or 420 months) on the left-hand side, and set it equal to the present value (the payments during the next 30 years) on the right-hand side. First, since deposits are monthly, determine the effective monthly interest rate during the first 35 years: j = 1.06” 12 — 1: 0.004868 Then, 1, 000 - Emflmgfis = 75, 000 - am: (1%“. = 18.403870 Using a calculator to solve for 1' gives 3.495%. ANS. (B) 32. Use each of the rates during its specified time period: 5 PV = 1,000 x (1.08)‘2 x exp(— f 0.015: dt) x (1 — 0.06)3 x (1.025)‘8 = 499.28 2 ANS. (D) 33. There is some extraneous information provided in this question—always a possibility on an actuarial exam. For a stock with dividends, the prepaid forward contract has an initial investment equal to the initial price of the stock, reduced for the anticipated dividends to be received during the investment period. Thus: F3} 2 Soc—5T = 802—034”) = 76.86 ANS. (B) 34. This problem can be done as a simple application of the quadratic formula. For example, assuming that j is the effective two—month interest rate: 2, 900 = 1, 000v} + 2, 0009}? J .r' — i i 2 .2 13.: ——1 + 3 =0.979837 4 , 1 j = — -— 1: 0.020578 0.979837 Copyright 2009 ASM. 9111 edition 651 Practice Exam 1 Then, since j is the two-month effective rate, the annual effective rate is: i=(1+j)6 — 1: .129994 ANS. (D) 35. Setting up the equivalency formula for the two yield equations: ~21-A = _2 0.50 x 80 _ TB 2 P — 120 + 0.03(O.50 x P) — 2 0.50 x P P = 94.21 ANS. (C) 652 Copyright © 2009 ASM. 9th edition ...
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This note was uploaded on 03/22/2012 for the course ACCOUNTING Intermedia taught by Professor Ghosh during the Spring '12 term at CUNY Baruch.

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